Problem: In parallelogram $ABCD$, angle $B$ measures $110^\circ$. What is the number of degrees in the measure of angle $C$?
[asy]
unitsize(1inch);
pair A,B,C,D;
B = (0,0);
C = (1,0);
A = rotate(100)*(0.6,0);
D = A+C;
draw(A--B--C--D--A);
label("$A$",A,N);
label("$D$",D,N);
label("$B$",B,S);
label("$C$",C,S);
[/asy] Because $\overline{AB}\parallel\overline{CD}$, we have $\angle B + \angle C = 180^\circ$.  Therefore, $\angle C = 180^\circ - \angle B = \boxed{70^\circ}$.